Hydrostatics is one of the sections of hydraulics that studies the equilibrium state of a fluid and the pressure that occurs in a fluid resting on various surfaces.
Hydrostatic pressure is a fundamental concept in hydrostatics. Consider a certain arbitrary volume of liquid in equilibrium. Inside this volume, we outline point A and mentally divide it in half with a plane passing through point A. On this plane, select a section with area S and center at point A. We remove one half of the volume and replace the force with which it acted on the remaining volume by balancing force F. Thus, the liquid in the second half will still be at rest.
Now we begin to reduce the area S so that point A is constantly inside it. With a sufficient decrease, point A coincides with pad S. And the pressure at point A will be determined by the formula P (A) = lim dF / dS as dS tends to zero.
Then the pressure exerted on the site S will be equal to the sum of the pressures exerted on all points belonging to this surface. That is, in other words: p = F / S. Hydrostatic pressure is a value equal to the quotient of dividing the force F by area S.
The cause of hydrostatic pressure is: the weight of the liquid itself and the pressure that is applied to the surface of the liquid. Thus, the pressure due to the very weight of the liquid and the external pressure are types of hydrostatic pressure. If the liquid is placed in the piston and a certain force is applied to it, then, naturally, the pressure inside the liquid will increase. Under normal conditions, atmospheric pressure exerts pressure on the fluid. If the pressure on the surface of the liquid is below atmospheric, then this pressure is called gauge.
A fluid is in equilibrium if all the pressure forces acting on any sufficiently small volume of fluid are balanced with each other.
Let us take a closer look at hydrostatic pressure and its properties:
- For any point arbitrarily taken in the liquid, the hydrostatic pressure vector is directed inside its volume and is perpendicular to the area allocated in the volume.
Let us prove this property: suppose that the angle at which the force is applied to a certain platform is not straight. We represent the force P as P (normal), P (tangent). Suppose that the tangent component is not equal to zero, then under its influence the liquid should flow along an inclined one, but it rests at a point. Hence the conclusion suggests itself that the tangent is equal to zero and the action of pressure occurs perpendicular to the site. The property is proven.
- The hydrostatic pressure is the same in all directions.
Let us prove this property of hydrostatic pressure: we select a tetrahedron in an arbitrary volume of liquid whose two planes coincide with the coordinate planes, and the third is chosen arbitrarily. At the base we get a right triangle. The action of the fluid on each face is denoted by: X * (P), Y * (P), Z * (P) The fluid is in equilibrium, so the total result of the action of all forces is 0.
E * (x) = 0
X * (P) dz âE * (P) de sin a = 0,
E * (y) = 0, E * (z) = 0
Z * (P) dx âE * (P) de cos a = 0
it is obvious that dz = de sin a, dx = de cos a
from here: X * (P) = E * (P), Z * (P) = E * (P)
output: X * (P) = Y * (P) = Z * (P) = E * (P)
The property is proven. Since the face was chosen arbitrarily, this equality is true for any case.
- Hydrostatic pressure varies in direct proportion to depth. As the depth increases, the pressure at the point will increase, and with a decrease in the depth of immersion, it will increase.
Any liquid point in equilibrium corresponds to the following equality: j + p / g = j (o) + p (o) / g = H, where j is the coordinate of this point, j (O) is the coordinate of the liquid surface, p and p (o) is the height of the columns, g is the specific gravity of the liquid, H is the hydrostatic pressure.
As a result of the transformations, we obtain: p = p (o) + g [j (0) âj] or p = p (o) + gh
where h is the immersion depth of a given point, and gh is nothing but the weight of a liquid column equal in height to h and having a unit in the base area. This property of hydrostatic pressure is called Pascal's Law.